# How does the Pauli exclusion principle apply to wave-particle duality?

Based on the Pauli exclusion principle , no two particles can have the same quantum state. However, in the double slit experiment with electrons (in which we observe wave-particle duality), at some points the wave functions add up to each other. In those specific spatial spots, two electrons have exactly the same quantum states, but not only do they not exclude each other, they are adding to the probability of each other's presence. How that is explained? Is this because only the two electrons with different spins are adding up to each other in this experiment? If so, I think the number of electrons in those specific points should be statistically half of the expected. Is that true?

• @QuantumBrick Suppose you have a large number of electrons. What then? Perhaps the answer is that the momenta of the various electrons will not be identical, and there is an enormous density of momentum states. I'm curious about this one. Aug 10, 2016 at 16:25
• The Pauli Exclusion Principle applies when you want to describe states with multiple fermions. When you do a double slit experiment you only deal with one fermion at a time. Each single fermion's wavefunction interferes with itself, but this has nothing to do with the PEP. Aug 10, 2016 at 16:30
• The statement "In those specific spatial spots, two electrons have exactly the same quantum states" is incorrect. First, in the typical double-slit experiment there is only one electron, and its wave function goes through both slits. Second, interference of wave functions from multiple particles does not mean that the two particles have the same state. Aug 10, 2016 at 17:08

Electrons only interfere with themselves. The dual slit experiment is basically a single electron case. Therefore Pauli exclusion dies not come into play. As to the question in the title, also particle wave duality is associated with single particles.

The text of your question implies that you have misunderstood the theoretical description of the Young's slits experiment. In the interference here, it is not two different electrons whose wavefunctions interfere, but two parts of the wavefuntion of each individual electron. Of course in practice many electrons may pass through the system, but each interferes with itself.

If it happened that more than two electrons approached the slits at the same time, then the Pauli exclusion principle would prevent them all having the same spatial wavefunction. That doesn't mean some would pass through one slit, some through another however. It means that the joint wavefunction would involve a sum of terms with each electron at both slits, but with various entanglements and minus signs between parts with electron labels swapped (I won't go into the details). However the more simple concept of Coulomb repulsion would already cause a big effect in this case.

If we were working with neutrons then there would be no Coulomb repulsion. With bright enough beams, Pauli exclusion would be relevant. There would still be interference etc. but the theoretical description would be more lengthy. One would have to write down a joint state for multiple neutrons; lots of entanglement as in previous paragraph.

The Pauli exclusion principle is an empirical result.

It's theoretically justified by positing fermionic and bosonic wave functions which are, respectively anti-symmetric and symmetric and which, respectively, gain a sign change or are unchanged when two particles are swapped, in the first case, two fermions, and in the latter, two bosons.

The phenomena of particle wave duality does not distinguish between the two cases, and applies to both; in fact, recall that particle-wave duality was first discovered with photons, and these are the gauge bosons of the Electromagnetic force, and it was the inspired idea of de Broglie that posited the same effect may occur with electrons, which are fermions, and when this idea was experimentally put to the tested, it was found to be the case.